Írj egy python függvényt, ami megvalósítja a következő függvényt (ahol $n$ egy pozitív egész szám, a függvény bemeneti változója): (0.5p) $$ f(n) = \begin{cases} \frac{n}{2} & \text{ha} \ n \ \text{páros}\\ 3 n + 1 & \text{ha} \ n \ \text{páratlan}\end{cases}$$
Írj egy python függvényt, aminek a bemenete egy pozitív egész szám $a_0$ és a kimenete egy lista, ami tartalmazza a következő sorozatot $a_k = f^k(a_0)$. A függvény addig iteráljon, amíg a sorazat el nem éri az 1-et. Például ha a bemenet $a_0 = 6$, akkor a függvény kimenete [6, 3, 10, 5, 16, 8, 4, 2, 1]. Figyelj arra, hogy a függvény ne léphessen végtelen ciklusba! Adj meg egy nagy számot, például 1000000-et, aminél a függvény nem iterálhat többet. Megjegyzés: $f^k$ az $f$ függvény $k$-szor önmagával vett kompozícióját jelöli. Például: $f^3(a_0) = f(f(f(a_0)))$. (0.5p)
Futtasd le a fentebb definiált függvényt az $a_0 = 1, 2, 3, \cdots, 10000$ számokra! Mit tapasztalsz? Van-e olyan szám, amire a függvény által generált sorozat nem éri el az 1-et? (0.5p)
Ábrázold $a_0$ függvényében a megállási időt ($a_0 = 1, 2, 3, \cdots, 10000$)! A megállasi idő $T$, az az egész szám, ahány iteráció szükséges hogy a sorazat elérje az 1-et, azaz $1 = f^T(a_0)$. Ábrázoláskor az adatpontok ne legyenek összekötve! (0.5p)
Mi volt a leghosszabb megállási idő, és melyik kezdeti értékhez tartozik? (0.5p)
def f(n): # definiálom a függvényt
if n%2==0: # megnézem páros-e
n=n/2 # ha az, akkor osztom 2-vel
else :
n=(3*n)+1 # ha nem, akkor megszorzom 3-al majd hozzáadok 1-et
return(n) # térjen vissza az értékkel
def ellenörző(n):
sorozat=[] # létrehozok egy üres listát
sorozat.append(n) # első elemem legyen az, amit megadok
for i in range(0,1000000): # nagyon sokszor megnézem majd *
if f(sorozat[i])!=1: # ha a megadott számomra hattatom a legelső kódom, és nem egy
sorozat.append(f(sorozat[i])) # akkor hozzáadom a sorozatomhoz
if len(sorozat)==1000000: # * de csak max ennyi darabszor
return(sorozat) # ha elértem a limitszámot akkor térjek vissza az eddigi eredményemmel
else:
sorozat.append(1) # amint a hattatásommal elérem az egyet, hozzáadom az 1-es számot
return(sorozat) # és vissza is térek a sorozatommal, a returnel megszakítom
for d in range(1,10000):# csinálok egy változót ami 1-től 10000-ig fut
print(ellenörző(d)) # ki is printelem. azt vettem észre, hogy mindig eléri az 1-et
[1, 4, 2.0, 1] [2, 1] [3, 10, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [4, 2.0, 1] [5, 16, 8.0, 4.0, 2.0, 1] [6, 3.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [7, 22, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [8, 4.0, 2.0, 1] [9, 28, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [10, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [11, 34, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [12, 6.0, 3.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [13, 40, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [14, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [15, 46, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [16, 8.0, 4.0, 2.0, 1] [17, 52, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [18, 9.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [19, 58, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [20, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [21, 64, 32.0, 16.0, 8.0, 4.0, 2.0, 1] [22, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [23, 70, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [24, 12.0, 6.0, 3.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [25, 76, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [26, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [27, 82, 41.0, 124.0, 62.0, 31.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [28, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [29, 88, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [30, 15.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [31, 94, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [32, 16.0, 8.0, 4.0, 2.0, 1] [33, 100, 50.0, 25.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [34, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [35, 106, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [36, 18.0, 9.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [37, 112, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [38, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [39, 118, 59.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [40, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [41, 124, 62.0, 31.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [42, 21.0, 64.0, 32.0, 16.0, 8.0, 4.0, 2.0, 1] [43, 130, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [44, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [45, 136, 68.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [46, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [47, 142, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [48, 24.0, 12.0, 6.0, 3.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [49, 148, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [50, 25.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [51, 154, 77.0, 232.0, 116.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [52, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [53, 160, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [54, 27.0, 82.0, 41.0, 124.0, 62.0, 31.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [55, 166, 83.0, 250.0, 125.0, 376.0, 188.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 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160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1941, 5824, 2912.0, 1456.0, 728.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1942, 971.0, 2914.0, 1457.0, 4372.0, 2186.0, 1093.0, 3280.0, 1640.0, 820.0, 410.0, 205.0, 616.0, 308.0, 154.0, 77.0, 232.0, 116.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1943, 5830, 2915.0, 8746.0, 4373.0, 13120.0, 6560.0, 3280.0, 1640.0, 820.0, 410.0, 205.0, 616.0, 308.0, 154.0, 77.0, 232.0, 116.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1944, 972.0, 486.0, 243.0, 730.0, 365.0, 1096.0, 548.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1945, 5836, 2918.0, 1459.0, 4378.0, 2189.0, 6568.0, 3284.0, 1642.0, 821.0, 2464.0, 1232.0, 616.0, 308.0, 154.0, 77.0, 232.0, 116.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1946, 973.0, 2920.0, 1460.0, 730.0, 365.0, 1096.0, 548.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1947, 5842, 2921.0, 8764.0, 4382.0, 2191.0, 6574.0, 3287.0, 9862.0, 4931.0, 14794.0, 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16.0, 8.0, 4.0, 2.0, 1] [1953, 5860, 2930.0, 1465.0, 4396.0, 2198.0, 1099.0, 3298.0, 1649.0, 4948.0, 2474.0, 1237.0, 3712.0, 1856.0, 928.0, 464.0, 232.0, 116.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1954, 977.0, 2932.0, 1466.0, 733.0, 2200.0, 1100.0, 550.0, 275.0, 826.0, 413.0, 1240.0, 620.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1955, 5866, 2933.0, 8800.0, 4400.0, 2200.0, 1100.0, 550.0, 275.0, 826.0, 413.0, 1240.0, 620.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1956, 978.0, 489.0, 1468.0, 734.0, 367.0, 1102.0, 551.0, 1654.0, 827.0, 2482.0, 1241.0, 3724.0, 1862.0, 931.0, 2794.0, 1397.0, 4192.0, 2096.0, 1048.0, 524.0, 262.0, 131.0, 394.0, 197.0, 592.0, 296.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1957, 5872, 2936.0, 1468.0, 734.0, 367.0, 1102.0, 551.0, 1654.0, 827.0, 2482.0, 1241.0, 3724.0, 1862.0, 931.0, 2794.0, 1397.0, 4192.0, 2096.0, 1048.0, 524.0, 262.0, 131.0, 394.0, 197.0, 592.0, 296.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1958, 979.0, 2938.0, 1469.0, 4408.0, 2204.0, 1102.0, 551.0, 1654.0, 827.0, 2482.0, 1241.0, 3724.0, 1862.0, 931.0, 2794.0, 1397.0, 4192.0, 2096.0, 1048.0, 524.0, 262.0, 131.0, 394.0, 197.0, 592.0, 296.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1959, 5878, 2939.0, 8818.0, 4409.0, 13228.0, 6614.0, 3307.0, 9922.0, 4961.0, 14884.0, 7442.0, 3721.0, 11164.0, 5582.0, 2791.0, 8374.0, 4187.0, 12562.0, 6281.0, 18844.0, 9422.0, 4711.0, 14134.0, 7067.0, 21202.0, 10601.0, 31804.0, 15902.0, 7951.0, 23854.0, 11927.0, 35782.0, 17891.0, 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5914, 2957.0, 8872.0, 4436.0, 2218.0, 1109.0, 3328.0, 1664.0, 832.0, 416.0, 208.0, 104.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1972, 986.0, 493.0, 1480.0, 740.0, 370.0, 185.0, 556.0, 278.0, 139.0, 418.0, 209.0, 628.0, 314.0, 157.0, 472.0, 236.0, 118.0, 59.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1973, 5920, 2960.0, 1480.0, 740.0, 370.0, 185.0, 556.0, 278.0, 139.0, 418.0, 209.0, 628.0, 314.0, 157.0, 472.0, 236.0, 118.0, 59.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1974, 987.0, 2962.0, 1481.0, 4444.0, 2222.0, 1111.0, 3334.0, 1667.0, 5002.0, 2501.0, 7504.0, 3752.0, 1876.0, 938.0, 469.0, 1408.0, 704.0, 352.0, 176.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1975, 5926, 2963.0, 8890.0, 4445.0, 13336.0, 6668.0, 3334.0, 1667.0, 5002.0, 2501.0, 7504.0, 3752.0, 1876.0, 938.0, 469.0, 1408.0, 704.0, 352.0, 176.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1976, 988.0, 494.0, 247.0, 742.0, 371.0, 1114.0, 557.0, 1672.0, 836.0, 418.0, 209.0, 628.0, 314.0, 157.0, 472.0, 236.0, 118.0, 59.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1977, 5932, 2966.0, 1483.0, 4450.0, 2225.0, 6676.0, 3338.0, 1669.0, 5008.0, 2504.0, 1252.0, 626.0, 313.0, 940.0, 470.0, 235.0, 706.0, 353.0, 1060.0, 530.0, 265.0, 796.0, 398.0, 199.0, 598.0, 299.0, 898.0, 449.0, 1348.0, 674.0, 337.0, 1012.0, 506.0, 253.0, 760.0, 380.0, 190.0, 95.0, 286.0, 143.0, 430.0, 215.0, 646.0, 323.0, 970.0, 485.0, 1456.0, 728.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1978, 989.0, 2968.0, 1484.0, 742.0, 371.0, 1114.0, 557.0, 1672.0, 836.0, 418.0, 209.0, 628.0, 314.0, 157.0, 472.0, 236.0, 118.0, 59.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1979, 5938, 2969.0, 8908.0, 4454.0, 2227.0, 6682.0, 3341.0, 10024.0, 5012.0, 2506.0, 1253.0, 3760.0, 1880.0, 940.0, 470.0, 235.0, 706.0, 353.0, 1060.0, 530.0, 265.0, 796.0, 398.0, 199.0, 598.0, 299.0, 898.0, 449.0, 1348.0, 674.0, 337.0, 1012.0, 506.0, 253.0, 760.0, 380.0, 190.0, 95.0, 286.0, 143.0, 430.0, 215.0, 646.0, 323.0, 970.0, 485.0, 1456.0, 728.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1980, 990.0, 495.0, 1486.0, 743.0, 2230.0, 1115.0, 3346.0, 1673.0, 5020.0, 2510.0, 1255.0, 3766.0, 1883.0, 5650.0, 2825.0, 8476.0, 4238.0, 2119.0, 6358.0, 3179.0, 9538.0, 4769.0, 14308.0, 7154.0, 3577.0, 10732.0, 5366.0, 2683.0, 8050.0, 4025.0, 12076.0, 6038.0, 3019.0, 9058.0, 4529.0, 13588.0, 6794.0, 3397.0, 10192.0, 5096.0, 2548.0, 1274.0, 637.0, 1912.0, 956.0, 478.0, 239.0, 718.0, 359.0, 1078.0, 539.0, 1618.0, 809.0, 2428.0, 1214.0, 607.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1981, 5944, 2972.0, 1486.0, 743.0, 2230.0, 1115.0, 3346.0, 1673.0, 5020.0, 2510.0, 1255.0, 3766.0, 1883.0, 5650.0, 2825.0, 8476.0, 4238.0, 2119.0, 6358.0, 3179.0, 9538.0, 4769.0, 14308.0, 7154.0, 3577.0, 10732.0, 5366.0, 2683.0, 8050.0, 4025.0, 12076.0, 6038.0, 3019.0, 9058.0, 4529.0, 13588.0, 6794.0, 3397.0, 10192.0, 5096.0, 2548.0, 1274.0, 637.0, 1912.0, 956.0, 478.0, 239.0, 718.0, 359.0, 1078.0, 539.0, 1618.0, 809.0, 2428.0, 1214.0, 607.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1982, 991.0, 2974.0, 1487.0, 4462.0, 2231.0, 6694.0, 3347.0, 10042.0, 5021.0, 15064.0, 7532.0, 3766.0, 1883.0, 5650.0, 2825.0, 8476.0, 4238.0, 2119.0, 6358.0, 3179.0, 9538.0, 4769.0, 14308.0, 7154.0, 3577.0, 10732.0, 5366.0, 2683.0, 8050.0, 4025.0, 12076.0, 6038.0, 3019.0, 9058.0, 4529.0, 13588.0, 6794.0, 3397.0, 10192.0, 5096.0, 2548.0, 1274.0, 637.0, 1912.0, 956.0, 478.0, 239.0, 718.0, 359.0, 1078.0, 539.0, 1618.0, 809.0, 2428.0, 1214.0, 607.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1983, 5950, 2975.0, 8926.0, 4463.0, 13390.0, 6695.0, 20086.0, 10043.0, 30130.0, 15065.0, 45196.0, 22598.0, 11299.0, 33898.0, 16949.0, 50848.0, 25424.0, 12712.0, 6356.0, 3178.0, 1589.0, 4768.0, 2384.0, 1192.0, 596.0, 298.0, 149.0, 448.0, 224.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1984, 992.0, 496.0, 248.0, 124.0, 62.0, 31.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1985, 5956, 2978.0, 1489.0, 4468.0, 2234.0, 1117.0, 3352.0, 1676.0, 838.0, 419.0, 1258.0, 629.0, 1888.0, 944.0, 472.0, 236.0, 118.0, 59.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1986, 993.0, 2980.0, 1490.0, 745.0, 2236.0, 1118.0, 559.0, 1678.0, 839.0, 2518.0, 1259.0, 3778.0, 1889.0, 5668.0, 2834.0, 1417.0, 4252.0, 2126.0, 1063.0, 3190.0, 1595.0, 4786.0, 2393.0, 7180.0, 3590.0, 1795.0, 5386.0, 2693.0, 8080.0, 4040.0, 2020.0, 1010.0, 505.0, 1516.0, 758.0, 379.0, 1138.0, 569.0, 1708.0, 854.0, 427.0, 1282.0, 641.0, 1924.0, 962.0, 481.0, 1444.0, 722.0, 361.0, 1084.0, 542.0, 271.0, 814.0, 407.0, 1222.0, 611.0, 1834.0, 917.0, 2752.0, 1376.0, 688.0, 344.0, 172.0, 86.0, 43.0, 130.0, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1987, 5962, 2981.0, 8944.0, 4472.0, 2236.0, 1118.0, 559.0, 1678.0, 839.0, 2518.0, 1259.0, 3778.0, 1889.0, 5668.0, 2834.0, 1417.0, 4252.0, 2126.0, 1063.0, 3190.0, 1595.0, 4786.0, 2393.0, 7180.0, 3590.0, 1795.0, 5386.0, 2693.0, 8080.0, 4040.0, 2020.0, 1010.0, 505.0, 1516.0, 758.0, 379.0, 1138.0, 569.0, 1708.0, 854.0, 427.0, 1282.0, 641.0, 1924.0, 962.0, 481.0, 1444.0, 722.0, 361.0, 1084.0, 542.0, 271.0, 814.0, 407.0, 1222.0, 611.0, 1834.0, 917.0, 2752.0, 1376.0, 688.0, 344.0, 172.0, 86.0, 43.0, 130.0, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1988, 994.0, 497.0, 1492.0, 746.0, 373.0, 1120.0, 560.0, 280.0, 140.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1989, 5968, 2984.0, 1492.0, 746.0, 373.0, 1120.0, 560.0, 280.0, 140.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1990, 995.0, 2986.0, 1493.0, 4480.0, 2240.0, 1120.0, 560.0, 280.0, 140.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1991, 5974, 2987.0, 8962.0, 4481.0, 13444.0, 6722.0, 3361.0, 10084.0, 5042.0, 2521.0, 7564.0, 3782.0, 1891.0, 5674.0, 2837.0, 8512.0, 4256.0, 2128.0, 1064.0, 532.0, 266.0, 133.0, 400.0, 200.0, 100.0, 50.0, 25.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1992, 996.0, 498.0, 249.0, 748.0, 374.0, 187.0, 562.0, 281.0, 844.0, 422.0, 211.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1993, 5980, 2990.0, 1495.0, 4486.0, 2243.0, 6730.0, 3365.0, 10096.0, 5048.0, 2524.0, 1262.0, 631.0, 1894.0, 947.0, 2842.0, 1421.0, 4264.0, 2132.0, 1066.0, 533.0, 1600.0, 800.0, 400.0, 200.0, 100.0, 50.0, 25.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1994, 997.0, 2992.0, 1496.0, 748.0, 374.0, 187.0, 562.0, 281.0, 844.0, 422.0, 211.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1995, 5986, 2993.0, 8980.0, 4490.0, 2245.0, 6736.0, 3368.0, 1684.0, 842.0, 421.0, 1264.0, 632.0, 316.0, 158.0, 79.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1996, 998.0, 499.0, 1498.0, 749.0, 2248.0, 1124.0, 562.0, 281.0, 844.0, 422.0, 211.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1997, 5992, 2996.0, 1498.0, 749.0, 2248.0, 1124.0, 562.0, 281.0, 844.0, 422.0, 211.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1998, 999.0, 2998.0, 1499.0, 4498.0, 2249.0, 6748.0, 3374.0, 1687.0, 5062.0, 2531.0, 7594.0, 3797.0, 11392.0, 5696.0, 2848.0, 1424.0, 712.0, 356.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [1999, 5998, 2999.0, 8998.0, 4499.0, 13498.0, 6749.0, 20248.0, 10124.0, 5062.0, 2531.0, 7594.0, 3797.0, 11392.0, 5696.0, 2848.0, 1424.0, 712.0, 356.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2000, 1000.0, 500.0, 250.0, 125.0, 376.0, 188.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2001, 6004, 3002.0, 1501.0, 4504.0, 2252.0, 1126.0, 563.0, 1690.0, 845.0, 2536.0, 1268.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2002, 1001.0, 3004.0, 1502.0, 751.0, 2254.0, 1127.0, 3382.0, 1691.0, 5074.0, 2537.0, 7612.0, 3806.0, 1903.0, 5710.0, 2855.0, 8566.0, 4283.0, 12850.0, 6425.0, 19276.0, 9638.0, 4819.0, 14458.0, 7229.0, 21688.0, 10844.0, 5422.0, 2711.0, 8134.0, 4067.0, 12202.0, 6101.0, 18304.0, 9152.0, 4576.0, 2288.0, 1144.0, 572.0, 286.0, 143.0, 430.0, 215.0, 646.0, 323.0, 970.0, 485.0, 1456.0, 728.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2003, 6010, 3005.0, 9016.0, 4508.0, 2254.0, 1127.0, 3382.0, 1691.0, 5074.0, 2537.0, 7612.0, 3806.0, 1903.0, 5710.0, 2855.0, 8566.0, 4283.0, 12850.0, 6425.0, 19276.0, 9638.0, 4819.0, 14458.0, 7229.0, 21688.0, 10844.0, 5422.0, 2711.0, 8134.0, 4067.0, 12202.0, 6101.0, 18304.0, 9152.0, 4576.0, 2288.0, 1144.0, 572.0, 286.0, 143.0, 430.0, 215.0, 646.0, 323.0, 970.0, 485.0, 1456.0, 728.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2004, 1002.0, 501.0, 1504.0, 752.0, 376.0, 188.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2005, 6016, 3008.0, 1504.0, 752.0, 376.0, 188.0, 94.0, 47.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2006, 1003.0, 3010.0, 1505.0, 4516.0, 2258.0, 1129.0, 3388.0, 1694.0, 847.0, 2542.0, 1271.0, 3814.0, 1907.0, 5722.0, 2861.0, 8584.0, 4292.0, 2146.0, 1073.0, 3220.0, 1610.0, 805.0, 2416.0, 1208.0, 604.0, 302.0, 151.0, 454.0, 227.0, 682.0, 341.0, 1024.0, 512.0, 256.0, 128.0, 64.0, 32.0, 16.0, 8.0, 4.0, 2.0, 1] [2007, 6022, 3011.0, 9034.0, 4517.0, 13552.0, 6776.0, 3388.0, 1694.0, 847.0, 2542.0, 1271.0, 3814.0, 1907.0, 5722.0, 2861.0, 8584.0, 4292.0, 2146.0, 1073.0, 3220.0, 1610.0, 805.0, 2416.0, 1208.0, 604.0, 302.0, 151.0, 454.0, 227.0, 682.0, 341.0, 1024.0, 512.0, 256.0, 128.0, 64.0, 32.0, 16.0, 8.0, 4.0, 2.0, 1] [2008, 1004.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2009, 6028, 3014.0, 1507.0, 4522.0, 2261.0, 6784.0, 3392.0, 1696.0, 848.0, 424.0, 212.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2010, 1005.0, 3016.0, 1508.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2011, 6034, 3017.0, 9052.0, 4526.0, 2263.0, 6790.0, 3395.0, 10186.0, 5093.0, 15280.0, 7640.0, 3820.0, 1910.0, 955.0, 2866.0, 1433.0, 4300.0, 2150.0, 1075.0, 3226.0, 1613.0, 4840.0, 2420.0, 1210.0, 605.0, 1816.0, 908.0, 454.0, 227.0, 682.0, 341.0, 1024.0, 512.0, 256.0, 128.0, 64.0, 32.0, 16.0, 8.0, 4.0, 2.0, 1] [2012, 1006.0, 503.0, 1510.0, 755.0, 2266.0, 1133.0, 3400.0, 1700.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2013, 6040, 3020.0, 1510.0, 755.0, 2266.0, 1133.0, 3400.0, 1700.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2014, 1007.0, 3022.0, 1511.0, 4534.0, 2267.0, 6802.0, 3401.0, 10204.0, 5102.0, 2551.0, 7654.0, 3827.0, 11482.0, 5741.0, 17224.0, 8612.0, 4306.0, 2153.0, 6460.0, 3230.0, 1615.0, 4846.0, 2423.0, 7270.0, 3635.0, 10906.0, 5453.0, 16360.0, 8180.0, 4090.0, 2045.0, 6136.0, 3068.0, 1534.0, 767.0, 2302.0, 1151.0, 3454.0, 1727.0, 5182.0, 2591.0, 7774.0, 3887.0, 11662.0, 5831.0, 17494.0, 8747.0, 26242.0, 13121.0, 39364.0, 19682.0, 9841.0, 29524.0, 14762.0, 7381.0, 22144.0, 11072.0, 5536.0, 2768.0, 1384.0, 692.0, 346.0, 173.0, 520.0, 260.0, 130.0, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2015, 6046, 3023.0, 9070.0, 4535.0, 13606.0, 6803.0, 20410.0, 10205.0, 30616.0, 15308.0, 7654.0, 3827.0, 11482.0, 5741.0, 17224.0, 8612.0, 4306.0, 2153.0, 6460.0, 3230.0, 1615.0, 4846.0, 2423.0, 7270.0, 3635.0, 10906.0, 5453.0, 16360.0, 8180.0, 4090.0, 2045.0, 6136.0, 3068.0, 1534.0, 767.0, 2302.0, 1151.0, 3454.0, 1727.0, 5182.0, 2591.0, 7774.0, 3887.0, 11662.0, 5831.0, 17494.0, 8747.0, 26242.0, 13121.0, 39364.0, 19682.0, 9841.0, 29524.0, 14762.0, 7381.0, 22144.0, 11072.0, 5536.0, 2768.0, 1384.0, 692.0, 346.0, 173.0, 520.0, 260.0, 130.0, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2016, 1008.0, 504.0, 252.0, 126.0, 63.0, 190.0, 95.0, 286.0, 143.0, 430.0, 215.0, 646.0, 323.0, 970.0, 485.0, 1456.0, 728.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2017, 6052, 3026.0, 1513.0, 4540.0, 2270.0, 1135.0, 3406.0, 1703.0, 5110.0, 2555.0, 7666.0, 3833.0, 11500.0, 5750.0, 2875.0, 8626.0, 4313.0, 12940.0, 6470.0, 3235.0, 9706.0, 4853.0, 14560.0, 7280.0, 3640.0, 1820.0, 910.0, 455.0, 1366.0, 683.0, 2050.0, 1025.0, 3076.0, 1538.0, 769.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2018, 1009.0, 3028.0, 1514.0, 757.0, 2272.0, 1136.0, 568.0, 284.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2019, 6058, 3029.0, 9088.0, 4544.0, 2272.0, 1136.0, 568.0, 284.0, 142.0, 71.0, 214.0, 107.0, 322.0, 161.0, 484.0, 242.0, 121.0, 364.0, 182.0, 91.0, 274.0, 137.0, 412.0, 206.0, 103.0, 310.0, 155.0, 466.0, 233.0, 700.0, 350.0, 175.0, 526.0, 263.0, 790.0, 395.0, 1186.0, 593.0, 1780.0, 890.0, 445.0, 1336.0, 668.0, 334.0, 167.0, 502.0, 251.0, 754.0, 377.0, 1132.0, 566.0, 283.0, 850.0, 425.0, 1276.0, 638.0, 319.0, 958.0, 479.0, 1438.0, 719.0, 2158.0, 1079.0, 3238.0, 1619.0, 4858.0, 2429.0, 7288.0, 3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2020, 1010.0, 505.0, 1516.0, 758.0, 379.0, 1138.0, 569.0, 1708.0, 854.0, 427.0, 1282.0, 641.0, 1924.0, 962.0, 481.0, 1444.0, 722.0, 361.0, 1084.0, 542.0, 271.0, 814.0, 407.0, 1222.0, 611.0, 1834.0, 917.0, 2752.0, 1376.0, 688.0, 344.0, 172.0, 86.0, 43.0, 130.0, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2021, 6064, 3032.0, 1516.0, 758.0, 379.0, 1138.0, 569.0, 1708.0, 854.0, 427.0, 1282.0, 641.0, 1924.0, 962.0, 481.0, 1444.0, 722.0, 361.0, 1084.0, 542.0, 271.0, 814.0, 407.0, 1222.0, 611.0, 1834.0, 917.0, 2752.0, 1376.0, 688.0, 344.0, 172.0, 86.0, 43.0, 130.0, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [2022, 1011.0, 3034.0, 1517.0, 4552.0, 2276.0, 1138.0, 569.0, 1708.0, 854.0, 427.0, 1282.0, 641.0, 1924.0, 962.0, 481.0, 1444.0, 722.0, 361.0, 1084.0, 542.0, 271.0, 814.0, 407.0, 1222.0, 611.0, 1834.0, 917.0, 2752.0, 1376.0, 688.0, 344.0, 172.0, 86.0, 43.0, 130.0, 65.0, 196.0, 98.0, 49.0, 148.0, 74.0, 37.0, 112.0, 56.0, 28.0, 14.0, 7.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 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8.0, 4.0, 2.0, 1] [3989, 11968, 5984.0, 2992.0, 1496.0, 748.0, 374.0, 187.0, 562.0, 281.0, 844.0, 422.0, 211.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3990, 1995.0, 5986.0, 2993.0, 8980.0, 4490.0, 2245.0, 6736.0, 3368.0, 1684.0, 842.0, 421.0, 1264.0, 632.0, 316.0, 158.0, 79.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3991, 11974, 5987.0, 17962.0, 8981.0, 26944.0, 13472.0, 6736.0, 3368.0, 1684.0, 842.0, 421.0, 1264.0, 632.0, 316.0, 158.0, 79.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3992, 1996.0, 998.0, 499.0, 1498.0, 749.0, 2248.0, 1124.0, 562.0, 281.0, 844.0, 422.0, 211.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3993, 11980, 5990.0, 2995.0, 8986.0, 4493.0, 13480.0, 6740.0, 3370.0, 1685.0, 5056.0, 2528.0, 1264.0, 632.0, 316.0, 158.0, 79.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3994, 1997.0, 5992.0, 2996.0, 1498.0, 749.0, 2248.0, 1124.0, 562.0, 281.0, 844.0, 422.0, 211.0, 634.0, 317.0, 952.0, 476.0, 238.0, 119.0, 358.0, 179.0, 538.0, 269.0, 808.0, 404.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3995, 11986, 5993.0, 17980.0, 8990.0, 4495.0, 13486.0, 6743.0, 20230.0, 10115.0, 30346.0, 15173.0, 45520.0, 22760.0, 11380.0, 5690.0, 2845.0, 8536.0, 4268.0, 2134.0, 1067.0, 3202.0, 1601.0, 4804.0, 2402.0, 1201.0, 3604.0, 1802.0, 901.0, 2704.0, 1352.0, 676.0, 338.0, 169.0, 508.0, 254.0, 127.0, 382.0, 191.0, 574.0, 287.0, 862.0, 431.0, 1294.0, 647.0, 1942.0, 971.0, 2914.0, 1457.0, 4372.0, 2186.0, 1093.0, 3280.0, 1640.0, 820.0, 410.0, 205.0, 616.0, 308.0, 154.0, 77.0, 232.0, 116.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3996, 1998.0, 999.0, 2998.0, 1499.0, 4498.0, 2249.0, 6748.0, 3374.0, 1687.0, 5062.0, 2531.0, 7594.0, 3797.0, 11392.0, 5696.0, 2848.0, 1424.0, 712.0, 356.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3997, 11992, 5996.0, 2998.0, 1499.0, 4498.0, 2249.0, 6748.0, 3374.0, 1687.0, 5062.0, 2531.0, 7594.0, 3797.0, 11392.0, 5696.0, 2848.0, 1424.0, 712.0, 356.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3998, 1999.0, 5998.0, 2999.0, 8998.0, 4499.0, 13498.0, 6749.0, 20248.0, 10124.0, 5062.0, 2531.0, 7594.0, 3797.0, 11392.0, 5696.0, 2848.0, 1424.0, 712.0, 356.0, 178.0, 89.0, 268.0, 134.0, 67.0, 202.0, 101.0, 304.0, 152.0, 76.0, 38.0, 19.0, 58.0, 29.0, 88.0, 44.0, 22.0, 11.0, 34.0, 17.0, 52.0, 26.0, 13.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1] [3999, 11998, 5999.0, 17998.0, 8999.0, 26998.0, 13499.0, 40498.0, 20249.0, 60748.0, 30374.0, 15187.0, 45562.0, 22781.0, 68344.0, 34172.0, 17086.0, 8543.0, 25630.0, 12815.0, 38446.0, 19223.0, 57670.0, 28835.0, 86506.0, 43253.0, 129760.0, 64880.0, 32440.0, 16220.0, 8110.0, 4055.0, 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4.0, 2.0, 1] [9994, 4997.0, 14992.0, 7496.0, 3748.0, 1874.0, 937.0, 2812.0, 1406.0, 703.0, 2110.0, 1055.0, 3166.0, 1583.0, 4750.0, 2375.0, 7126.0, 3563.0, 10690.0, 5345.0, 16036.0, 8018.0, 4009.0, 12028.0, 6014.0, 3007.0, 9022.0, 4511.0, 13534.0, 6767.0, 20302.0, 10151.0, 30454.0, 15227.0, 45682.0, 22841.0, 68524.0, 34262.0, 17131.0, 51394.0, 25697.0, 77092.0, 38546.0, 19273.0, 57820.0, 28910.0, 14455.0, 43366.0, 21683.0, 65050.0, 32525.0, 97576.0, 48788.0, 24394.0, 12197.0, 36592.0, 18296.0, 9148.0, 4574.0, 2287.0, 6862.0, 3431.0, 10294.0, 5147.0, 15442.0, 7721.0, 23164.0, 11582.0, 5791.0, 17374.0, 8687.0, 26062.0, 13031.0, 39094.0, 19547.0, 58642.0, 29321.0, 87964.0, 43982.0, 21991.0, 65974.0, 32987.0, 98962.0, 49481.0, 148444.0, 74222.0, 37111.0, 111334.0, 55667.0, 167002.0, 83501.0, 250504.0, 125252.0, 62626.0, 31313.0, 93940.0, 46970.0, 23485.0, 70456.0, 35228.0, 17614.0, 8807.0, 26422.0, 13211.0, 39634.0, 19817.0, 59452.0, 29726.0, 14863.0, 44590.0, 22295.0, 66886.0, 33443.0, 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3644.0, 1822.0, 911.0, 2734.0, 1367.0, 4102.0, 2051.0, 6154.0, 3077.0, 9232.0, 4616.0, 2308.0, 1154.0, 577.0, 1732.0, 866.0, 433.0, 1300.0, 650.0, 325.0, 976.0, 488.0, 244.0, 122.0, 61.0, 184.0, 92.0, 46.0, 23.0, 70.0, 35.0, 106.0, 53.0, 160.0, 80.0, 40.0, 20.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1]
def T(n): # létrehozok egy változót
megállási=[] # kell egy lista
for d in range(1,n+1): #egytől tizezerig akarom csinálni
megállási.append(len((ellenörző(d)))) # hozzáadom a listához a d-edig lista karakterhosszát(hány számból érte el)
return(megállási) # meg is nézetem
hossz=T(10000) #létrehozok egy változóz, ami a 10000-ig tartalmazza listaként a függvény értékeit
eddigilegmagasabb=1 # egy változó ami az eddigi legmagasabbak tárolja
for i in range(0,10000):
éppeni=hossz[i]
if éppeni > eddigilegmagasabb: # ha az új vizsgált szám nagyobb
eddigilegmagasabb=éppeni # akkor kicserélem arra a legelső változómat
print(eddigilegmagasabb-1) # meg is nézem mi az
261
T(d).index(262)+1 # mivel 0-val kezdődik az indexelés, ezért -1,ik szám lesz az, mint amit kiír
6171